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- di Bernardo, M., et al.
(författare)
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Bifurcations of dynamical systems with sliding : derivation of normal-form mappings
- 2002
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Ingår i: Physica D. - 0167-2789 .- 1872-8022. ; 170:04-mar, s. 175-205
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Tidskriftsartikel (refereegranskat)abstract
- This paper is concerned with the analysis of so-called sliding bifurcations in n-dimensional piecewise-smooth dynamical systems with discontinuous vector field. These novel bifurcations occur when the system trajectory interacts with regions on the discontinuity set where sliding is possible. The derivation of appropriate normal-form maps is detailed. It is shown that the leading-order term in the map depends on the particular bifurcation scenario considered. This is in turn related to the possible bifurcation scenarios exhibited by a periodic orbit undergoing one of the sliding bifurcations discussed in the paper. A third-order relay system serves as a numerical example.
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| 4. |
- Di Bernardo, M., et al.
(författare)
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Sliding bifurcations : A novel mechanism for the sudden onset of chaos in dry friction oscillators
- 2003
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Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 13:10, s. 2935-2948
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Tidskriftsartikel (refereegranskat)abstract
- Recent investigations of nonsmooth dynamical systems have resulted in the study of a class of novel bifurcations termed as sliding bifurcations. These bifurcations are a characteristic feature of so-called Filippov systems, that is, systems of ordinary differential equations (ODEs) with discontinuous right-hand sides. In this paper we show that sliding bifurcations also play an important role in organizing the dynamics of dry friction oscillators, which are a subclass of nonsmooth systems. After introducing the possible codimension-1 sliding bifurcations of limit cycles, we show that these bifurcations organize different types of slip to stick-slip transitions in dry friction oscillators. In particular, we show both numerically and analytically that a sliding bifurcation is an important mechanism causing the sudden jump to chaos previously unexplained in the literature on friction systems. To analyze such bifurcations we make use of a new analytical method based on the study of appropriate normal form maps describing sliding bifurcations. Also, we explain the circumstances under which the theory of so-called border-collision bifurcations can be used in order to explain the onset of complex behavior in stick-slip systems.
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- Laurie, Andrew D., et al.
(författare)
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The role of the alarmone (p)ppGpp in sigma N competition for core RNA polymerase
- 2003
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Ingår i: Journal of Biological Chemistry. - : American Society for Biochemistry and Molecular Biology. - 0021-9258 .- 1083-351X. ; 278:3, s. 1494-1503
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Tidskriftsartikel (refereegranskat)abstract
- Some promoters, including the DmpR-controlled sigma(N)-dependent Po promoter, are effectively rendered silent in cells lacking the nutritional alarmone (p)ppGpp. Here we demonstrate that four mutations within the housekeeping sigma(D)-factor can restore sigma(N)-dependent Po transcription in the absence of (p)ppGpp. Using both in vitro and in vivo transcription competition assays, we show that all the four sigma(D) mutant proteins are defective in their ability to compete with sigma(N) for available core RNA polymerase and that the magnitude of the defect reflects the hierarchy of restoration of transcription from Po in (p)ppGpp-deficient cells. Consistently, underproduction of sigma(D) or overproduction of the anti-sigma(D) protein Rsd were also found to allow (p)ppGpp-independent transcription from the sigma(N)-Po promoter. Together with data from the direct effects of (p)ppGpp on sigma(N)-dependent Po transcription and sigma-factor competition, the results support a model in which (p)ppGpp serves as a master global regulator of transcription by differentially modulating alternative sigma-factor competition to adapt to changing cellular nutritional demands.
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